A318871 Minimum Heinz number of a factorization of n into factors > 1.

1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 41, 43, 47, 49, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset

1,2

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 = the empty product.
a(12) = 35 = 5 * 7 = prime(3) * prime(4).
a(16) = 49 = 7^2 = prime(4)^2.
a(23) = 83 = prime(23).

Maple

a:= proc(n) option remember; `if`(n=1, 1, min(seq(a(d)*
      ithprime(n/d), d=numtheory[divisors](n) minus {n})))
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Sep 05 2018

Mathematica

facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]];
Table[Min[Times@@Prime/@#&/@facs[n]], {n, 100}]

Crossrefs

Cf. A000040, A001055, A007716, A056239, A064988, A162247, A215366, A246868.

Sequence in context: A242393 A210494 A338483 * A330225 A275938 A093893

Adjacent sequences: A318868 A318869 A318870 * A318872 A318873 A318874

Keyword

nonn

Author

Gus Wiseman, Sep 05 2018

Status

approved